The great abstract ideas (considered directly and not merely in tacit use) which have dominated the science were due to them - namely, ratio, irrationality, continuity, the point, the straight line, the plane.
In 1761 he proved the irrationality of 7r; a simpler proof was given somewhat later by Legendre.
In one of the notes Legendre gives a proof of the irrationality of 7r.
This property is referred to as the "irrationality of dispersion."
The irrationality of dispersion is well illustrated by C.Christiansen's experiments on the dispersive properties of white powders.
Lambert, 1 " read before the Berlin Academy in 1761, in which he demonstrated the irrationality of 7r.
The general test of irrationality which he established is that, if a l a, a, be an interminate continued fraction, a l, a2,
This want of proportion in the dispersion for different regions of the spectrum is called the "irrationality of dispersion"; and it is as a direct consequence of this irrationality, that there exists a secondary spectrum or residual colour dispersion, showing itself at the focus of all such telescopes, and roughly in proportion to their size.
These glasses, however, still hold the field, although glasses are now produced whose irrationality of dispersion has been reduced to a very slight amount.
Moreover the greater depths of the curves (or "curvature powers") in itself neutralize more or less the advantages obtained from the reduced irrationality of dispersion.